Aself-portrait by the master of the genre, Rembrandt van Rijn, is to become the focus of a grubby battle between the UK art world and an American museum, with the public roped in. All this will be conducted in the dramatic language of "saving" it for the "nation", as if it were at risk.

The work, which shows, unusually, an exuberant and laughing Rembrandt, is a tronie – a head study – which depicts an emotional state. It is thought to have been painted in 1628, making it an early work by the artist, of which Britain has few. It has only recently been attributed to him, having languished in a private collection until 2007, when it was bought at auction for £2.2m – rather more than the modest estimate of £1,500 – as it was no longer seen as a copy. With a formal change in identification soon after, it has since become an object of desire accompanied by an escalating price tag. The Getty Museum, in California, has made an offer to purchase it for £16.5m.

If the painting goes to America it won't be lost. It's not going back into the closed world of a private collection and would be a nice addition to an institution which has the money to acquire and care for it, which, after all, is what matters. But this possibility is a loss too great for our culture minister. Ed Vaizey has placed an export ban on the work. Now public museums and galleries are being encouraged to bid to keep it in the UK. They need to meet the Getty's offer. At the postcard-size of 23.75 X 17cm, that's about £40,867 per cm squared. You have to ask: is the small but perfectly formed Rembrandt worth this sum? And, what is the cost of trying to keep it?

There is no doubt that Rembrandt is one of the greatest artists who ever lived. It's difficult to put a price tag on that. There won't be anyone like him again so any scrap of canvas is worth treasuring. And it is a picture that lifts one's spirit. Nor do I think that the arts should fall off our list of priorities in difficult economic times. A civilised society should support schools, hospitals, and art galleries.

But there is a risk that these inflated sums damage our appreciation of the art work. The high price tags become the subject of conversation and attention, rather that the piece itself. Soon this painting will be spoken of only in terms of how many dollars or pounds it fetched, the brush strokes that bring to life the head will become secondary. Just look at the Mona Lisa. Or rather, ask yourself if you can. Consider the never-ending queues down multiple corridors to view that great painting; the thick glass case that obscures it; and the difficulty we have in just seeing it unencumbered by the baggage of money and fame.

The true value of these celebrity paintings: like Picasso's Child with a Dove, which left Britain when the Qatar royal family bought it for £50m, is tarnished by massive sums. The relativistic climate of judgment when it comes to the arts, today – where everyone's opinion is valid – combined with an overreliance on economic value as a proof of worth, means we are handing over the valuing of art to the market. This inevitably distorts rather than enhances our appreciation of great work.

When I spend time outside the major museums and galleries, visiting collections that are less well known, I can relax and enjoy the paintings in a way it is difficult to do in the pressured environment where the approach taken is to showcase the greatest hits; the most expensive. Only where there is little talk of money and fame is it possible to truly see the work on the walls. It is time to rethink what we invest in for the nation.